A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916427824365568 |
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| author | Qian, Yixiao Li, Weizhen Tan, Yan Zhang, Qinghai |
| author_facet | Qian, Yixiao Li, Weizhen Tan, Yan Zhang, Qinghai |
| contents | We propose a fourth-order cut-cell method for solving Poisson's equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable to arbitrarily complex geometries, (b) high order discretization, (c) optimal complexity. Feature (a) is achieved by Yin space, which is a mathematical model for three-dimensional continua. Feature (b) is accomplished by poised lattice generation (PLG) algorithm, which finds stencils near the irregular boundary for polynomial fitting. Besides, for feature (c), we design a modified multigrid solver whose complexity is theoretically optimal by applying nested dissection (ND) ordering method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05865 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains Qian, Yixiao Li, Weizhen Tan, Yan Zhang, Qinghai Numerical Analysis We propose a fourth-order cut-cell method for solving Poisson's equations in three-dimensional irregular domains. Major distinguishing features of our method include (a) applicable to arbitrarily complex geometries, (b) high order discretization, (c) optimal complexity. Feature (a) is achieved by Yin space, which is a mathematical model for three-dimensional continua. Feature (b) is accomplished by poised lattice generation (PLG) algorithm, which finds stencils near the irregular boundary for polynomial fitting. Besides, for feature (c), we design a modified multigrid solver whose complexity is theoretically optimal by applying nested dissection (ND) ordering method. |
| title | A fourth-order, multigrid cut-cell method for solving Poisson's equation in three-dimensional irregular domains |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2410.05865 |